J . Am. Chem. SOC.1991, 113, 5114-5116
5114
mode. The quantity is the full width at half maximum for the individual vibronic components, and Eo is the energy of the 0 0 vibronic transition for the mode h w . We have utilized the results of emission spectral fitting to calculate AGO from AGO = (E, (Ayop,l/2)2/16ksTIn 2)awplor - (EO+ (AF!,l/2)2/16kBTIn 2)In this equation the band width at half maximum is related to A’, as shown in eq 2. The quantity A’ is the sum of reorganizational energies for the solvent and the averaged, low-frequency vibrational mode treated classically.
-
+
A’ = (AFo,l/2)2/16kBTIn 2
(2)
The quenching scheme involves the series of reactions in eq 3.12.’5-’6b A kinetic analysis based on this scheme gives the 0s”
*+Q
k-d
0s”
*, Q
%
OsII, 3Q
20sI1 + 3Q
(3)
relationships shown in eqs 4a and 4b. In applying these equations, kq = kd/(l + k-d/ket + l/Ket) kc,
(4a)
= (KA(l/kq - ( l + Ket)/kdKe~~l-~
(4b)
it was assumed that k4 = k’-d and the relationships in eqs 5 and 6 were ~ti1ized.l~ KA = kd/k-d k,,/k,,
= K,, = exp -(AGo/RT)
(6)
k,,(calcd) = ( 2 r p / h ) F ( c a l c d )
2 2 [exp(-S,.)]
Acknowledgment is made to the NSF for support of this research under Grant No. CHE-8806664, to the Ministry of Human Resource and Development, Government of India, for fellowship support for Z.M., to the US.Department of Defense for fellowship support for D.G., and to Professor D. G. Whitten for pointing out the possible role of the second triplet excited state of 2,3-benzanthracene. (19) (a) Barqawi, K.; Llobet, A.; Meyer, T. J. J . Am. Chem. Soc. 1988, 110,7751. (b) Barqawi, K.; Murtaza, Z.; Meyer, T. J. J . Phys. Chem. 1991, 95, 47.
(5)
A quantum mechanically derived expression for k,, is shown in eq 7. It is based on the coupling to the energy-transfer process of averaged, medium-frequency, ring-stretching modes in the donor ( m ) and acceptor (n)and low-frequency and solvent modes treated classically.%*16In eq 7b, S, and S,. are the electron-vibrational
F(calcd) = [1/(4rA’kBT)1/2]
energy transfer because, in forming the lowest triplets of anthracene and 2,3-benzanthracene, the maximum rate constant is below the diffusion-controlled limit. The second is that, as for electron transfer, higher lying, accessible excited states can interfere with the observation of inverted behavior in energy transfer. Finally, it is possible to utilize structural and energetic parameters derived from emission spectral profiles to calculate relative rate constants for energy transfer. This approach has been utilized to calculate relative rate constants for nonradiative decay for MLCT excited states including polypyridyl complexes of 0 s ” and It may have additional applications elsewhere.
Reaction of a Distorted Amide with Nucleophilic Thiolate-Containing Zwitterions Produced from Thiolamines. A Model for the Acylation Step in Cysteine Proteases and Transglutaminases J. W. Keillor and R. S.Brown*
Department of Chemistry, University of Alberta Edmonton, Alberta, Canada T6G 2G2 Received February 21, 1991
(7a) X
n*=O ma0
Distorted amide 1 (2,3,4,5-tetrahydro-2-0~01,5-ethanobenz[exp(-S,)] (S$ / n * ! )( S z / m ! )x azepine)] has been shown to be susceptible toward bifunctional [exp{-(AGo + A’12 + n’hw + m h ~ ) ~ / 4 X ’ ~ ~(7b) k ~ g ] nucleophiles such as B-amino alcohols2 and certain dicarboxylic acids3 as simple model systems for the serine and aspartate procoupling constants. The sums are over the ground-state vibrational teases, respectively. Herein, we report the reactions of 1 with levels of the donor ( m ) and the excited-state vibrational levels of P-amino thiols which can be taken as a simple model for the third the acceptor (n*). The terms in the sums past n* = 4 and m = of the four classes of proteases, namely, the cysteine proteases‘ 4 were negligible. (and phenomenologically similar transgl~taminases~). In Figure 1 is shown a calculated plot of log k, vs AGO for the The maximum rate of disappearance of 1 in the presence of data with anthracene as quencher. The line was calculated by thiolamines 2a-c occurs a t pH levels above the value of pKthiol using eq 4a with kd = 9.1 X lo9 M-’s-I and kd/k4 = 2.3,” eq and lower than the value of pKNH+so that the zwitterionic am6 to calculate Kcl, and eq 7 to calculate ket. In the calculation monium thiolate is the active attacking species.6 Alkyl thiols of k,, average values of S (1.2) and X‘ (1860 cm-I) were utilized for the complexes with h w = 1300 cm-1.8 The parameters for ( I ) Somayaji, V. S.;Brown, R. S.J . Org. Chem. 1986, 51, 26762686, anthracene were taken from the emission spectral fitting results. (2) Skorey, K. 1.; Somayaji, V.;Brown, R. S.;Ball, R. G. J . Org. Chem. The quantity is the average value for the complexes (A’’’) 1986, 51,4866-4872. (3) Somayaji, V.;Keillor, J. W.; Brown, R. S. J . Am. Chem. Soc. 1988, and A’ for anthracene (A’22), Al12 = + X’22)/2 = 1090 cm-l. 110,2625-2629. The magnitude of the energy exchange matrix element, V, used (4) (a) Glazer, A. N.; Smith, E. L. In The Enzymes;Boyer, P. P., Ed.; in eq 7 to calculate the line was V = 4 cm-I. This is consistent Academic Press: New York. 1971; Vol. 3, pp 502-546. (b) Drenth, J.; with literature values found for energy transfer involving organic Jansonius, J. N.; Koekoek, R.; Wolthers, B. G.In The Enzymes; Boyer, P. P., Ed.;Academic Press: New York, 1971; Vol. 3, pp 484-499. (c) Liu, T.-Y.; triplets.’* Elliott, S.D. In The Enzymes;Boyer, P. P., Ed.; Academic Press: New York, Several important conclusions emerge from our results. The 1971; Vol. 3, pp 609-647. (d) Mitchell, W. M.;Harrington, W. F. In The first is that the inverted region can be reached for energy transfer Enzymes; Boyer, P. P., Ed.; Academic Press: New York, 1971; Vol. 3, pp as well as for electron transfer. It is more easily observed for 699-719. (e) Brocklehurst, K. Merhods Enzymol. 1982,87c, 427-469. (f) ( I S ) (a) Rehm, D.; Weller, A. Eer. Bunsen-Ges. Phys. Chem. 1969, 73, 834. (b) Balzani, V.;Bolleta, F.; Scandola, F. J . Am. Chem. Soc. 1980, 102, 2152. (16) (a) Ulstrup, J.; Jortner, J. J . Chem. Phys. 1975, 63, 4358. (b) Orlandi, G.;Monte, S.; Barigelletti, F.; Balzani, V. Chem. Phys. 1980, 52, 313. (17) An average association constant K A = k /kd = 2.3 was calculated by using the Eigen-Fuoss equation, KA = 4dV&/3000, with d = r 11 rQ; No is Avogadro’s number. In the calculations the values rail = 7.6 Rand rQ 2.2 A were used. (18) (a) Saltiel, J.; Khalil, G.E.; Schanze, K. Chem. Phys. Len. 1980, 70, 33. (b) Birks, J. B. Phorophysics ofAromaric Molecules; Wilcy-Interscience: New York, 1970; Chapter 2.
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+
0002-7863/91/ 1513-5 114$02.50/0
PolgHr, L.; HalBsz, P. Eiochem. J. 1982,207, 1-10. (8) Baker, E. N.; Drenth, J. Eiol. Macromol. Assem. 1987,3,313-368. (h) PolgHr, L.Acra Biochlm. Eiophys. Hung. 1988,23,207-213. (i) PolgBr, L. Eiol. Chem. Hoppe-Seylcr 1990, 371, 327-331. ( 5 ) (a) Folk, J. E.; Chung, S.I. Merhods Enzymology 1985,113,358-375. (b) Schrode, J.; Folk, J. E. J . Eiol. Chem. 1978, 254, 653-661. (c) Gross, M.; Wheteel, N. K.; Folk, J. E. J . Biol. Chem. 1977, 252, 3752-3579. (d) Folk, J. E.; Cole, P. E.; Mullooly, J. P. J . Eiol. Chem. 1967, 242,4329-4333. (6) Previous small-molecule biomimetic studies have been reported to model acyl transfer from esters to zwitterionic ammonium thiolates: (a) Street, J. P.; Brown, R. S.J. Am. Chem. Soc. 1985, 107, 6084-6089. (b) Skorey, K. 1.; Brown, R. S.J . Am. Chem. Soc. 1985, 107, 4070-4072. (c)
Street, J. P.; Skorey, K. I.; Brown, R. S.; Ball, R. G. J . Am. Chem. Soc. 1985, 107, 7669-7679.
0 1991 American Chemical Society
J. Am. Chem. SOC.,Vol. 113, No. 13, 1991 5115
Communications to the Editor Table 1. kZmXand Kinetic pKthioI Values of the Reactions of Various Thiols with Distorted Amide 1 [T= 25 OC, p = 1.0 (KCI)]
Scheme I
k,MX,u kinetic lit. lit. M--! s-1 PKtbioll) PKthbl PKamino 99.2 8.37 8.35c 10.86c 30.5 7.73 7.74d 10.89d
thiol 2a. cysteamine 2b; (k,N-dimethylamino)ethanethiol
ZC, 4-(2-mercaptoethyl)morpholine 1.47
6.49 6.57' 9.55' 0.36 8.03' k,3-mercaptopropionitrile
